It was the Rays' second victory in a win-or-go-home road contest in three days. They won at Texas on Monday in a tiebreaker to decide the AL's second wild card.

Rays starter Alex Cobb worked 6 2/3 gritty innings and Desmond Jennings delivered the big hit, a two-run double in the fourth inning. Fernando Rodney worked a perfect ninth to close out the victory.

Tampa Bay will take on the top-seeded Boston Red Sox in Game 1 of the ALDS at Fenway Park on Friday.

Cobb, who missed a chunk of the regular season after he was hit in the head by a line drive, quieted a thundering Cleveland crowd and ended the Indians' unexpected season.

"Can't put into words the appreciation I have celebrating on this field," Cobb said. "I knew how close it was to not coming back. Sitting on the couch watching these games, I knew we had a good chance. We have a great team. I was going to do everything I could to get back and be a part of it."

Delmon Young homered in the third inning off rookie Danny Salazar for the Rays, who were playing in their third city over four days (they won in Toronto on Sunday to force a tiebreaker).

Fernando Rodney later struck out Lonnie Chisenhall to end it. Rodney dropped to one knee, pointed skyward and soon was mobbed by all the Rays, who may be a little homesick (they've traveled 3,627 miles since leaving home on Sept. 23) but are Boston-bound.

"Go out and play our game," Jennings said. "It's going to be tough anytime you play Boston."

The Indians went from 94 losses a year ago to 92 wins under first-year manager Terry Francona and won their last 10 games to make the postseason for the first time since 2007.